document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030968>Question 1030968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Level 3:  Three teachers have provided you with an equation that models their salaries in million of dollars each year. \r<BR>\n" );
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document.write( "Teacher A:  A(x) = 4x + 50\r<BR>\n" );
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document.write( "Teacher B:  B(x) = 2x2 + 31\r<BR>\n" );
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document.write( "Teacher C:  W(x) = 2x - 5\r<BR>\n" );
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document.write( "During which years does Teacher A make the most money?  Between what two years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645874 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Teacher A:  A(x) = 4x + 50<BR>\n" );
document.write( "Teacher B:  B(x) = 2x2 + 31<BR>\n" );
document.write( "Teacher C:  W(x) = 2x - 5<BR>\n" );
document.write( "Teacher A will always make more than Teacher C,<BR>\n" );
document.write( "So let's first see when the salary for A and B are<BR>\n" );
document.write( "equal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+50+=+2x%5E2+%2B+31 ALIGN=MIDDLE  ALT=\"4x+%2B+50+=+2x%5E2+%2B+31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add -4x -50 to each side<BR>\n" );
document.write( "0 = 2x^2 - 4x - 19<BR>\n" );
document.write( "The quadratic formula provides the following solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-sqrt%2821%2F2%29 ALIGN=MIDDLE  ALT=\"1-sqrt%2821%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%2821%2F2%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%2821%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-sqrt%2821%2F2%29 ALIGN=MIDDLE  ALT=\"1-sqrt%2821%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, so the root of interest<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%2821%2F2%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%2821%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximately 4.24<BR>\n" );
document.write( "From this we can say that in year 5 Teacher A<BR>\n" );
document.write( "will make more than Teacher B.  This will also<BR>\n" );
document.write( "be true for years beyond 5 </SPAN>\n" );
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